easy: in MATLAB

mam2sug: Transform Mamdani Fuzzy Inference System into Sugeno Fuzzy Inference System

Syntax: sug_fis=mam2sug(mam_fis)

enjoy

it should be noted that it is a zero order TSK (constant)

Ali Chaibakhsh> it should be noted that it is a zero order TSK (constant)

To add to Ali's contribution, in principle there is a functional equivalence between Mamdani and Sugeno under certain conditions.  Namely the conditions are first, all Mamdani rules have consequent membership functions which are (or are collapsed into) fuzzy singletons (e.g. {5/1.0}).  This is equivalent to zero order Sugeno where the rule consequents are constants (e.g.  y=5) which is the second condition.

The literature contains several papers that prove this functional equivalence.  In addition, it has been proved that Mamdani (with singleton consequent MF's), Sugeno zero order, and RBF neural-networks are all functionally equivalent under these constraints.

Finally, TSK is in theory not limited to zero order or linear, but can be any order.

This is rather strange question. What do you expect from this? At any case, both methods are approximation of a continuous function and from this point of view they are equivalent. Of course, you can take the result of Mamdani's (after defuzzification) and then form TS-rules with constants. But what for?

If you want to obtain good result of function approximation then better use the Fuzzy transform -see, e.g.,

@article{perf:FSS06ftransf,

author = {Perfilieva, I.},

year = {2006},

title = {Fuzzy Transforms: theory and applications},

journal = {Fuzzy Sets and Systems},

volume = {157},

pages = {993-1023}

}

and many other papers on its applications (cf. google). This method works perfectly, it is easy to implement, it is computationally effective and you always know what's happening (this is not the case with TS rules).

Vilem Novak